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 A133520 Smallest k such that p(n)^4 + k is prime where p(n) is the n-th prime. 8
 1, 2, 6, 10, 12, 10, 16, 16, 6, 12, 18, 16, 12, 28, 6, 22, 6, 16, 6, 16, 6, 16, 30, 6, 16, 42, 22, 42, 28, 52, 22, 16, 28, 10, 28, 70, 30, 42, 78, 36, 12, 42, 6, 12, 40, 12, 12, 16, 16, 16, 18, 10, 6, 22, 60, 46, 76, 46, 18, 126, 12, 22, 22, 6, 16, 16, 22, 18, 120, 22, 12, 6, 6, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE p(2)=3, 3^4 = 81; for odd k and n > 1, p(n)^r + k is even and thus not prime, so we only need consider even k. for k = 2: 81 + 2 = 83, which is prime, so 2 is the smallest number that can be added to 81 to make a new prime. Hence a(2) = 2. MATHEMATICA NextPrime[#]-#&/@(Prime[Range[80]]^4) (* Harvey P. Dale, May 17 2015 *) CROSSREFS Cf. A030814, A054271, A091666, A133517, A133518, A133519, A133521, A133522, (A001223). Sequence in context: A125241 A116043 A085258 * A346299 A099017 A298748 Adjacent sequences:  A133517 A133518 A133519 * A133521 A133522 A133523 KEYWORD easy,nonn AUTHOR Carl R. White, Sep 14 2007 STATUS approved

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Last modified August 19 09:28 EDT 2022. Contains 356227 sequences. (Running on oeis4.)